Welcome to the forum!
Let's get you running first, then you can deal with keys & lock cylinder.
This is a typical setup, as I do not know your specific model. If you look closely at the front body panel cover there are some screws that come from the rear side to the front to hold it on. Take your time and don't rush locating them all. The screws are Phillips head #2 usually.
You need to remove that front body panel (the top black one in the photo, if yours is like this model), look @ the ignition lock cylinder & switch- follow the wiring from the switch to the first connector block- that can be 3, 4, or 5 wires. Disconnect ALL of those wires.
Now your scooter will kick start to run, and turn off by the "kill switch" just above the start button.
After your scooter is running again, take the two key halves to a locksmith or a place that cuts keys and see if they can make a new one. if they can't you'll need to replace the lock cylinder / switch. remove the 2 8mm hex head bolts hold it in place, plus there is a small plastic collar that can be removed by twisting counter clockwise on the side where the key inserts
CAUTION - only attempt this next part if you have some electrical circuit knowledge. or take a close photo of the switch harness and attach it to a post for guidance
If you have a jumper wire, the red and black wires from the scooter harness can be jumped and this will allow it to crank through the start button.
Do NOT connect the green wire or the black with the white tracer wire.